Time is an important but complex area of learning for students in the primary years. This study sought to develop a tool which would provide a clear picture of students' understanding of what constitutes time and how time is related to clock and calendar use. Four major components of time, Awareness of time, Succession, Duration, and Measurement…

A challenge for prospective teachers (PTs) is to determine what students know about a topic through asking appropriate questions and being thoughtful about the wording of these questions so as to capture and reframe students' spontaneous mathematical thinking and eventually unriddle the fuzzy boundary of students' complex thinking. This study…

Sensitive topics evaluation presents both a maze and a minefield to qualitative evaluators due to their complexity and their potential to create areas of misanalysis. For novice and experienced qualitatve practitioners alike, the evaluator can find the task of broaching complex content and developing trusting relationships to be serious…

This study aimed to apply the novel use of a conceptual interview and flowchart to support teachers in easily identifying areas of development in writing using the developmental/cognitive model of writing (Flower & Hayes, 1980). This study involved two phases. The first phase involved the creation of a conceptual interview and flowchart based…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

While spatial reasoning skills have been found to predict mathematical achievement, little is known about how primary students' conceptual understanding of three-dimensional objects develops. This paper reports insights into a Year 4 student's spatial reasoning when constructing and describing the properties of rectangular prisms, using Froebel's…

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers' and students' inverse function meanings. Responding to this call, we characterize 25 pre-service teachers' inverse function meanings as inferred from our analysis of clinical interviews. After…

One well-known learning obstacle is that students rarely use the concepts in the way that scientists use them. Rather, students mix up closely related concepts and are inclined towards matter-based conceptualisations. Furthermore, some researchers have argued that certain difficulties are rooted in the student's limited repertoire of causal…

In 2001-2002, the authors of this article interviewed 31 ethno-culturally diverse doctoral students about their experiences in a sociology of education program at a Canadian university. Approximately 10 years later, in a second qualitative study, we had the chance to conduct semi-structured interviews with 13 of the former students to find out…

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

In this article, attempts were made to examine students' thinking about the concepts of infinity and their ideas about transiting from finite to infinite states through the concept of limits of sequences. The participants included 78 senior high-school students ranging in age between 17 and 19 years old. The data were collected through a…

Background: An increased awareness of how people with intellectual disabilities (ID) understand death and dying is necessary in supporting life-long learning, post-bereavement support and planning end-of-life care. Previous research suggests that adults with ID have a limited or "patchy" understanding of the basic biological components…

While many university students take science courses in multiple disciplines, little is known about how they perceive common concepts from different disciplinary perspectives. Structure-property and structure-function relationships have long been considered important explanatory concepts in the disciplines of chemistry and biology, respectively.…

When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while…

This chapter argues that expert practice is an inquiry that surfaces a hermeneutic relationship between theory, practice, and the world, with implications for new lines of questioning in the Decoding interview.